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NEET 2015
Exam
NEET
Year
2015
Subject
Physics
Chapter
Work, Power and Energy

NEET 2015 · Physics · Work, Power and Energy

A particle of mass m is driven by a machine that delivers a...

A particle of mass mm is driven by a machine that delivers a constant power kk watts. If the particle starts from rest the force on the particle at time tt is:

Options

  1. Amk2t−12\sqrt{\dfrac{mk}{2}}{t}^{- \dfrac{1}{2}}
  2. Bmkt−12\sqrt{mk}{t}^{- \dfrac{1}{2}}
  3. C2mkt−12\sqrt{2mk}{t}^{- \dfrac{1}{2}}
  4. D12mkt−12\dfrac{1}{2}\sqrt{mk}{t}^{- \dfrac{1}{2}}

Correct answer

A. mk2t−12\sqrt{\dfrac{mk}{2}}{t}^{- \dfrac{1}{2}}

Step-by-step solution

(Fv= constant =kSo,mdvdtv=k⇒∫vdv=∫kmdt⇒v22=kmt⇒v=2kmt\begin{aligned} & F v=\text{ constant }=\mathrm{k} \\ & \mathrm{So}, \\ & \frac{\mathrm{mdv}}{\mathrm{dt}} \mathrm{v}=\mathrm{k} \\ \Rightarrow & \int \mathrm{vdv}=\int \frac{\mathrm{k}}{\mathrm{m}} \mathrm{dt} \\ \Rightarrow & \frac{\mathrm{v}^2}{2}=\frac{\mathrm{k}}{\mathrm{m}} \mathrm{t} \\ \Rightarrow & \mathrm{v}=\sqrt{\frac{2 \mathrm{k}}{\mathrm{m}} \mathrm{t}} \end{aligned}) Now, (F=mdvdt=m2km12t−12=mk2t−12\begin{aligned} & F=\frac{\mathrm{mdv}}{\mathrm{dt}} \\ & =\mathrm{m} \sqrt{\frac{2 \mathrm{k}}{\mathrm{m}}} \frac{1}{2} \mathrm{t}^{-\frac{1}{2}} \\ & =\sqrt{\frac{\mathrm{mk}}{2}} \mathrm{t}^{-\frac{1}{2}} \end{aligned})
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